Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 2

✍ Scribed by Laurent Cairó; Jaume Llibre

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 840 KB
• Volume: 67
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2006.04.021

✦ Synopsis

We classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 2. In other words we characterize all the global phase portraits of the quadratic polynomial vector fields having all their orbits contained in conics. For such a vector field there are exactly 25 different global phase portraits in the Poincaré disc, up to a reversal of sense.